SME
Environmental Engineering
Solid waste
Use this for “A town of 50,000 throws away 2 kg a person a day, compacted to 600 kg/m³ with 0.25 cover. How long does a 1.52 × 10⁶ m³ landfill last, and how much land at 20 m deep?”
Diagram
Each slice of the bar is one year’s use, 76,041.6667 m³.
1.52 ×
10
6
76,041.6667
=
19.99:
the
reserve
lasts
19.99
years
if
use
stays
the
same.
This is an example. Type your own values to start a new problem.
Vᵧ (m³/yr)
=
365
×
P (people)
×
r (kg/(person·d))
×
(1
+
)
ρ (kg/m³)
t (yr)
=
C (m³)
Vᵧ (m³/yr)
A (m²)
=
C (m³)
D (m)
Formulas
Vᵧ
=
365
×
P
×
r
×
1 +
c
ρ
76,042
=
365
×
50,000
×
2
×
1 + 0.25
600
t
=
C
Vᵧ
19.99
=
1.52 ×
10
6
76,042
A
=
C
D
76,000
=
1.52 ×
10
6
20
Assumptions
•
The population and the waste each person makes stay steady over the life of the site.
•
Cover ratio c: daily cover soil as a share of the compacted waste volume.
•
A year is 365 days; the site is filled to a uniform depth D over its area.
Step-by-step
WE KNOW
P = 50,000 people, r = 2 kg/(person·d), ρ = 600 kg/m³, c = 0.25, C = 1.52 × 10⁶ m³, D = 20 m
FIND
volume a year (Vᵧ), site life (t), site area (A)
Step 1 · Find volume a year (Vᵧ)
Use Vᵧ = 365 × P × r × (1 + c) ÷ ρ
The year’s waste in kg, divided by the density for its volume, plus the cover soil on top.
Vᵧ
=
365
×
50,000
×
2
×
1 + 0.25
600
Vᵧ
=
365
×
50,000
×
2
×
1.25
600
Vᵧ
=
18,250,000
×
2
×
1.25
600
Vᵧ
=
36,500,000
×
1.25
600
Vᵧ
=
45,625,000
600
Vᵧ = 76,042 m³/yr
Step 2 · Find site life (t)
Use t = C ÷ Vᵧ
How many years of waste the site holds.
t
=
1.52 ×
10
6
76,042
t
=
19.99
yr
Step 3 · Find site area (A)
Use A = C ÷ D
The capacity spread to the fill depth covers this much ground.
A
=
1.52 ×
10
6
20
A
=
76,000
m²
Check
Put the numbers back in. Both sides should match.
76,042
=
365
×
50,000
×
2
×
1 + 0.25
600
✓
19.99
=
1.52 ×
10
6
76,042
✓
76,000
=
1.52 ×
10
6
20
✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
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